Sometimes you have to break from the pattern. A lot of times you'll see the pattern designer tell you to knit with a circular needle up to a certain point, begin the decreases, and switch to double points when it gets too tight. You'll also see patterns which require two different sets of circular needles. I suspect this is the case with yours. I think the pattern designers do this so you'll have to buy more needles, more money for their company.
You can knit the ribbing with a smaller needle and switch to a larger one, but you don't have to. You can knit the ribbing with the larger needle and go on to the stockinette from there. It'll be a tad bit looser, but won't make a whole lot of difference. When I knit mittens, I knit the cuff and the rest of the mitten with one size needle. It's just because I have interchangeables and I'm too lazy to switch them. lol I find that the mittens are actually easier to get on that way, as the cuffs are looser.
One thing I would suggest for hats, mittens, and sock cuffs is that you cast on with a German Twisted Cast On. This makes the edge stretchy so it's easier to get on over the head, hand, and foot. If you use a standard long tail cast on, the hat may not go over the head at all.
I'd like to make a personal suggestion. Knit the baby hat in all rib stitch. I've made hats like this with the top part in stockinette. They drive me crazy because the hats are always riding up on me and twisting around. An all-ribbed hat fits the head better and stays put. Here's a pattern. I think it's done on straight needles, but I don't see why you couldn't do this in magic loop.